Applicability of TRG to non-Abelian gauge theories with fermions in 1+1 dimensions

Determine whether the tensor renormalization group (TRG) method is applicable to non-Abelian gauge theories coupled to fermions in 1+1 dimensions, by establishing its validity and effectiveness for such systems.

Background

The tensor renormalization group (TRG) is attractive for lattice gauge theory studies because it avoids the sign problem and enables direct estimation of partition functions at finite density. It has been successfully used across various lattice models and dimensions, including extracting conformal field theory data at criticality.

Despite these successes, extending TRG to non-Abelian gauge theories with dynamical fermions has been challenging. The paper explicitly notes that TRG’s applicability to such systems is not established even in 1+1 dimensions, motivating their work on constructing Grassmann tensor network representations and applying bond-weighted TRG to two-color QCD in 1+1 dimensions.

References

The applicability of the method to non-Abelian gauge theories coupled to fermions remains unclear, even in $(1+1)$ dimensions.

— Two-color lattice QCD in $(1+1)$ dimensions with Grassmann tensor renormalization group (2501.18918 - Pai et al., 31 Jan 2025) in Section 1 Introduction